Data Representation

4 Key excerpts on "Data Representation"

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  eBook - ePub

  Understanding Quantitative Data in Educational Research

  • Nicoleta Gaciu(Author)
  • 2020(Publication Date)
  • SAGE Publications Ltd

    (Publisher)

  3 Graphical representation of data Chapter Objectives In this chapter, we will: introduce the concept of graphical representation of educational data present key principles for the graphical representation of data consider the essential features of different methods to visualise quantitative data understand how to create and work with tables and graphs in R correctly demonstrate examples from educational research to illustrate the use of graphs and tables for different types of variables and scales of measurement. The graphical representation of data is the process of transformation of data into information through a wide range of graphical displays, including graphs, maps, pictograms and tables in a symbolic representation. This process is a vital part of data analysis that facilitates the process of identifying, interpreting and understanding patterns or trends, which may not be visible in the raw data. It is also a useful and accurate communication tool for a range of educational stakeholders. A proper understanding of graphical display is one of the most important aspects of data analysis for students, teachers and researchers, helping them to avoid mistakes when summarising large data sets and analysing relevant patterns in quantitative data. For anyone engaged in educational research, it is very helpful to find relevant patterns in the graphical representation of data before performing any statistical tests or transforming statistical values into more meaningful concepts. The graphical representation of data depends on the type of quantitative data. For example, to organise and summarise categorical data, a bar graph can be used. For a time series, a line graph is recommended. Small data sets are usually easier to interpret if data is displayed in tabular form

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  eBook - ePub

  Mental Models

  • Dedre Gentner, Albert L. Stevens, Dedre Gentner, Albert L. Stevens(Authors)
  • 2014(Publication Date)
  • Psychology Press

    (Publisher)

  Table 5.12 . The striking feature about this section is its emphasis on a mathematical equation-based representation.

  Table 5.12 Table of Kinematics Relations Given in Halliday and Resnick (1966)

  In summary, it doesn't seem surprising that students who have studied a text similar to that discussed in the preceding pages tend not to construct or to use physical representations. In this case the physical representation discussed (graphs) was both confusing and not relevant to the problems. The material most relevant to the problems was in completely mathematical form. The subject herself made no interpretations of the equations that might have been used in making physical representations.

  IV. Summary

  Most individuals can mentally represent a simple physical situation sufficiently well that they can make simple inferences about what will happen next. I have described here an analog to this ability to construct naive representations, an ability which begins to account for how skilled individuals reason qualitatively or intuitively about complex situations. This physical representation, in contrast to naive representations, has the following features:

  • The entities are technical, with meaning only in physics.
  • The inferencing rules are qualitative.
  • The inferencing rules are time-independent and redundant.
  • The representation is closely associated with fundamental principles of physics.
  • Properties of the entities are localized to those entities.

  This representation was illustrated by preliminary versions of rules for creating and extending two kinds of physical representations (force and work-energy).

  Empirical studies relevant to this conceptualization of expertise include the order in which experts and novices access principles in solving simple problems, and the extent and nature of the qualitative discussion preceding any quantitiative work on a more difficult problem. In the easy problems, experts seemed to use principles in an order dictated by the schemas they were completing, whereas novices either followed an order based on a mathematical formula or were unable to do the problem. In more difficult cases, experts seemed to assess whether a schema could be completed without contradictions before doing any quantitative work. Once this was ascertained, then the quantitative work proceeded uneventfully.

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  eBook - ePub

  The Aesthetics of Scientific Data Representation

  More than Pretty Pictures

  • Lotte Philipsen, Rikke Schmidt Kjærgaard, Lotte Philipsen, Rikke Schmidt Kjærgaard(Authors)
  • 2017(Publication Date)
  • Taylor & Francis

    (Publisher)

  6 The Epistemics of Data Representation How to Transform Data into Knowledge Nina Samuel

  Following the question of a visualization of the invisible of the previous chapter, this chapter zooms in from something that is very big and very far away (i.e. outer space) to something that is extremely small and as close to us as possible: microscopic images of human cells. Switching from the macro-cosmos to the micro-cosmos, we are confronted with a very similar problem: The phenomena are interpreted visually – given a concrete visual form – by accumulating and handling large amounts of mathematical data. In both cases, we are dealing with three distinct elements that are in a relation to each other but that need to be neatly distinguished: a phenomenon that is investigated (e.g. a star, a galaxy, a cell), data gained from this phenomenon through a technological device, and finally a representation – usually an image – based on an interpretation of the data (often referred to as “image processing” or “manipulation”). This chapter focuses on how these three elements relate to each other, and especially, how data measurements are transformed into visual representation and how they actively participate in the formation of theories. It is a key assumption of this chapter that representations have the power to actively influence the direction of scientific research and shape the development of scientific hypotheses and that representations can provide experts with new insights about their field (see Bredekamp, Dünkel & Schneider, 2015). This is called the epistemic function of representation. Images are no ornament in the scientific discourse; they are no retroactive visualization of existing facts. On the contrary, they are crucial for the decision on what becomes a “fact” and what is discarded from the scientific discourse.

  The Quest for Increasing Resolution

  This epistemic function of representation can be observed through centuries. The development of different microscopic techniques has informed our knowledge of cells’ structures and functions at all times. Media employed to visualize these structures and technical expertise has shaped biological thought and our image of nature (cf. Bruhn, 2011). As a prominent example, the shift from electron microscopy to electronic light microscopy (i.e. video microscopy) has directed biologists’ view of the cell away from the static view (where terms like “architecture” and “skeleton” were used for biological structures) to a new dynamic one and to a completely new understanding of living cells (Breidenmoser et al., 2010, 19–22). The following will ask in which way the recently invented method of localization microscopy contributes to an understanding of the epistemics of biological imaging and data visualization in general – and to the relation of the three elements mentioned above (phenomenon, data, and representation).

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  eBook - ePub

  The Nature of Scientific Thinking

  On Interpretation, Explanation and Understanding

  • J. Faye(Author)
  • 2016(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  W , the mathematical model corresponding to the conceptual model. To be understood, the representation of the physical system idealizes reality, stripping away most of the observed features, and focusing on only a few, considered the most salient. A conceptual model is represented by a structure (a token of a type or a model of an original.) A conceptual model is an idealized copy of the actual physical structure. All instances of representational relationships and abstract/concrete structures may be observed in a scientific explanation.

  As an example, Debs and Redhead explain how modern physics uses a representational structure regarding X -radiation: “Modern physics models this phenomenon with the concept of an electromagnetic wave. This wave-like behavior may be modeled through the use of orthogonal sinusoidal functions summarized in Maxwell’s equations.”23 Thus scientists try to represent a physical phenomenon by introducing a model that allows them to discuss what the phenomenon is and what it is isn’t, and how it should be understood. In this case, the idealized model of the phenomenon is electromagnetic waves visualized via orthogonal sinusoidal functions. The most salient features observed by the scientist in relation to a physical phenomenon have been represented by a concrete scientific structure, the mathematical model.

  As Giere points out, it is of course important to choose the right features to include in the representational relation.24 At least initially, the scientist is unlikely to know which features are “right”; thus, in the real world there are most likely to be a variety of competing models, and the one which wins out – by virtue of being used most frequently – comes to be seen as the one which chose the “right” features. Within the social dimension of representation, the information relation is important. Here, this relation holds between two scientists, as opposed to two structures. A feature of the physical world, W

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